Electromechanical wave filter



' DecQll, 1956 w, P, MASON Er AL 2,774,942

ELECTROMECHANICAL WAVE FILTER Filed April 29, 1953 VENTOR'S F? MASON NH. J. MC S/(lM/N ATTORNEY United States Patent ELECTROMECHANICAL WAVEFILTER Warren P. Mason, West Orange, and Herbert J. McSkimin,

Basking Ridge, N. J., assignors to Bell Telephone Laboratories,Incorporated, New York, N. Y., a corporation of New York ApplicationApril 29, 1953, Serial No. 351,842

7 Claims. (Cl. 333-71) This invention relates to mechanical wave filtersand more particularly to those filters which are torsionally excited.

The principal object of this invention is to improve the frequencyfiltering characteristics of a mechanical wave filter.

One common form of mechanical wave filter consists of a relatively long,small-diameter rod of acoustic material and one or more members ofgreater diameter centrally connected thereto and adapted to be set intoflexural vibration when longitudinal vibrations are impressed upon oneend of the rod. Peaks of attenuation occur at the antiresonantfrequencies of the transverse members and these peaks are usuallylocated close to the frequency pass band limits to obtain sharp cut-ofrcharacteristics. In such a filter, however, when certainsignals areapplied, spurious resonances resulting from mechanical coupling to otherthan the longitudinal mode of vibration appear and, as a consequence,the output signals are undesirably distorted in these instances.Previous to this invention, various ways, including operating the filterat low signal levels or making the frequency cut-ofi characteristicsless sharp, have been tried for the purpose of eliminating thisdifiiculty butso far as is known none has proved as satisfactory asmight be wished. The present invention is directed to a simple andinexpensive solution of this problem by means which also permit verysharp frequency cut-ofis and substantial signal levels.

In accordance with the present invention in one embodiment thereof asmall-diameter rod of acoustic mate rial of length I has connected toits midpoint a larger diameter thin disk or plate of a similar materialwhich vibrates in a torsional mode when an angular rotational torque isapplied to one end of the rod. By properly dimensioning this centrallylocated disk, as, for example, in accordance with the formulas set forthherein, a peak of attenuation can be placed either above or below thefrequency pass band at a chosen frequency, thereby facilitating almostany desired degree of sharpness in the cut-off characteristics.

The nature of this invention will be more fully understood from thefollowing detailed description given in connection with the accompanyingdrawings, in which:

Fig. 1 is a perspective view of a mechanical wave filter in accordancewith the invention employing a centrally positioned disk;

Fig. 2 is a diagram of the electrical equivalent of the mechanicalfilter shown in Fig. 1; and

Fig. 3 is a perspective view of a cascaded mechanical wave filter inaccordance with the invention.

Referring now particularly to the drawings, Fig. 1 shows, for thepurposes of illustration, as an embodiment of the invention mechanicalfilter which consists of a small-diameter rod 11 of a suitable acousticmaterial to which is connected disk or plate 12 of a similar or likematerial. This disk is fastened to rod 11 substantially midway betweenthe ends thereof and is preferably, though not necessarily, formed as anintegral part. Since disk 12 is the principal resonating element of thefilter, its mechanical Q should be as high as possible in order tominimize loss and also to minimize loss distortion in the pass band andconsequently to improve the cut-off characteristics of the filter.Accordingly it should be chosen from a low loss material such as anickel-iron alloy although in many, if not all, applications certainceramics or crystals are well suited.

The dimensions of rod 11 and disk 12 will most conveniently be set forthin connection with the formulas characterizing the electrical behaviorof the equivalent circuit shown in Fig. 2. It should be noted here,however, that the dimensions of filter 10 for a given frequency ofoperation in the torsional mode are entirely difierent from those of afilter having the same operating frequency but excited in a longitudinalmode. One noticeable difference is that the length of filter 10 isapproximately only one-half that of a comparable longitudinal modefilter.

Fig. 2 shows the electrical analogue of the mechanical filter shown inFig. 1. This electrical equivalent circuit consists of two identicalwave transmission lines 21 and 22, each having a length l/2 which isapproximately a quarter wavelength long at the frequency of operation,whose adjacent ends are joined together by a serially connected paralleltuned circuit 23. The image propagation constant 0 and image impedanceZ1 for the filter are given by the following S111 v Z0 OS 27) Z Lsinlsin I) Z9 21) where v is the velocity of propagation along the line, Iis the total length of both sections of line, Z0 is the characteristicimpedance of each line, to is angular frequency, Zs is the impedance ofthe resonant circuit 23 given by [L is the shear modulus in the acousticmaterial and p is the density. p p

The series impedance ZS for disk 12 near its antiresonant frequencyvibrating in a torsional mode is jail z.-

where f is frequency r .4636r1v f.

r is the inner radius of disk 12 and r2 is the outer radius, I1=1.559(r2 -r1 )h, and h is the thickness of disk 12, these distances incentimeters.

For the case where fr, the anti-resonant frequency of disk 12, liesbelow the frequency pass band, it can be shown from the above equationsthat the image impedance at mid-band is :1 l jiflm t t 8 luff-PG (twa n)r where fu is the upper cut-off frequency corresponding to cosh 0=--1 inEquation 1, fl. is the lower cut-off frequency corresponding to cosh0=+1 in Equation 1,

Similarly it can be'sho'wn that where fr lies above the upper cut-offfrequency shown in Fig. 3. may be used. As shown, two filters,

one having a peak above and the other below the band, may be connectedin series. As discussed above, the dimensions of each section of thefilter may be determined from Equations 5 and 6. By thus cascadingfilter sections of the type shown in Fig. 1, increasingly sharp cutoffcharacteristics may be obtained. Although filter 10 will havetransmission bands in addition to the principal one considered here,these may, if objectionable, be eliminated by attenuation provided bythe torsional input and output transducers used in conjunction with thefilter.

It should be understood that the invention described herein is notlimited to wholly mechanical systems but will be very useful inelectromechanical filters such as telephone channel frequency-separatingfilters and superheterodyne radio receiver intermediate-frequencyfilters. These electromechanical devices of course require transducers,such as described in 'Electro-Mechanical Transducers and Wave Filters byW. P. Mason, Van Nostrand Company, 1948, to convert the electricalsignals into the vibrations applied to the mechanical filters.

Changes and modifications in the illustrative embodiment describedherein will occur to those skilled in the art and may be made withoutdeparting from the spirit or scope of the invention.

What is claimed is: r

1. A mechanical wave filter for transmitting a band of frequencies, saidfilter having a lower cut-off frequency in, and an upper cut-offfrequency f0, comprising a small-diameter cylindrical rod of acousticmaterial of radius r1 having a length I that is approximately a halfwavelength long in the torsional mode of vibration at a frequency withinsaid band, and an annular disk of acoustic material of distributed masshaving an inner radius r1, an outer radius rz, and a thickness h that isless than one-half wavelength in the torsional mode of vibration at afrequency within 'said band connectedto said rod and dimensioned toresonate in a single torsional mode at a frequency ifr when said *rod istorsionally excited by mechanical vibrations applied to an end thereof,whereby a peak of attenuation is provided at a frequency fr at a desiredpoint outside the pass band of said filter. I

2.'The combination of elements as in claim I in which said disk is anintegral part of said rod.

3. The combination of elements in claim 1 in which.

said disk is positioned symmetrically-on said rod midway between theends thereof. v 4. A cascaded mechanical wave filter comprising aplurality of mechanical filters connectedin-series; each filter'like thefilter in claim 1, at least one of said filters having its annular diskresonant at a frequency differing from the resonant frequencies of thecorresponding disks of the other filters to give a peak of attenuationoutside the pass band jwhereby there is a peak of attenuation i aboveand a peak below the band cut-off frequencies.

5; 'A mechanical wave filter comprising awave filterlike the filter inclaim -1, means for'impressing torsional vibrations on one end of saidrod, and means for receiving torsional vibrations at the other end ofsaid rod.

6. A mechanical wave filter for transmitting a preassigned band offrequencies comprising means includ-C ing a rodof acoustic materialhaving -'a length approximately equal to a half w'aveleng'thinthetorsional mode of vibration at a frequency within said =pre'assignedfband for transmitting a band of frequencies including saidpreassigned band, and-means for .producing 'apeakyof I attenuation at afrequency close to one -limit-=-of fsaid preassigned ,band, saidlast-mentioned means including a transverse thincon'tinu'ou's annularmember made of acoustic material of distributed mass cent-rally mountednear the center of said rodan'ddimensioned to resonate in a torsionalmode at the frequency of said peak of attenuation when said rod istorsionally excited bymechanical vibrations applied to an end thereof. U

7. A mechanical wave filtera's in claim 1 coupled to a torsionalelectromechanical transducer, in which the image impedance la in thetorsional mode of vibration of said mechanical wave filter is matched tothe output mechanical impedance of said torsional mechanical transducer.v i

References Cited in the tile of this patent UNITED STATESJ'PATENTS i

